This BJS study came out in Jan. 2019
Source And Use Of Firearms Involved In Crimes: Survey Of Prison Inmates, 2016
https://www.bjs.gov/content/pub/pdf/suficspi16.pdf
Table 5 is the Source of Firearms table and here is the money quote dealing with straw purchasers,
"About a quarter (26%) of state prisoners and about a fifth (21%) of federal prisoners obtained a
firearm that they possessed during their offense from an individual in a non-retail setting, such as a friend or
family member." and
" Among prisoners who possessed a firearm when they committed the offense for which they were imprisoned
and who reported the source from which they obtained it, the most common source (43%) was on-the-street or
the underground market (table 5). Another 7% of state and 5% of federal prisoners stole the firearm, and 7%
of state and 8% of federal prisoners reported that they obtained the firearm at the location of the crime."
Now, remember that surveying prisoners who are engaged in various illegal actions may fudge a bit on the truth, especially when locked up and potential admission to other crimes. Particularly, the incidence of using stolen weapons is probably higher than prisoner interviews would indicate,
" More than 237,000 guns nationwide were reported stolen to the National Crime Information Center in 2016, a database maintained by the FBI. That represents a 68 percent increase in stolen weapons reported to the FBI since 2005. Some of the increase may be attributed to better reporting from local law enforcement.
The FBI database suggests nearly two million weapons have been stolen around the country in the last decade."
https://www.washingtontimes.com/news/2017/dec/2/analysis-lost-stolen-guns-used-in-thousands-of-cri/
Guns Used in Crime report from the BJS is a bit old (1995) but has some good information on stolen firearms,
https://www.bjs.gov/content/pub/pdf/GUIC.PDF
The more recent Report of Firearms Stolen in Household Burglaries is a bit more recent
https://www.bjs.gov/content/pub/pdf/fshbopc0510.pdf
And this research, done using Pittsburg PA data,
http://www.socialmedicine.info/index.php/socialmedicine/article/view/852/1649
indicated that about 30 percent of the firearms were stolen.
"After recovery and when police made contact with owners, more than 30 percent of the
firearms were said to have been stolen (n = 292, 32.7%), yet only 169 of those (57.9%) had been
officially reported stolen prior to recovery by police (Table 1). Of the 292 stolen firearms, the police
could not always determine if the owner of the stolen firearm knew the thief. Forty-nine (16.8%)
said they did and 33 (11.3%) said they did not. Police determined that in 88 cases the owner
reported the theft to an insurance company, and in 74 cases they did not."